Research involved the development of novel neurodynamical models of neurons and networks comprising the respiratory neural control system as studied experimentally in parallel in the rodent brain. Data-based models developed included (1) biophysically realistic cellular-level computational models of respiratory neurons incorporating current information on cellular architecture and biophysical properties such as ionic conductance mechanisms underlying neuronal activity, and (2) large-scale models of brainstem respiratory neural networks incorporating available information on network functional and structural architecture. The overall objective of these modeling studies was to gain mechanistic insights into the manner in which cellular- and circuit-level properties are integrated into microcircuits as well as large-scale respiratory networks for dynamical operation of the mammalian respiratory neural control system. A new model of respiratory central pattern generation (CPG) networks in the rodent brainstem was developed consisting of interacting excitatory and inhibitory subnetworks distributed in serially arranged brainstem structural compartments, each with distinct functional roles in generation and control of the respiratory neural activity patterns that evolve during the normal breathing cycle of inspiration followed by expiration. The basic network architecture and cellular properties used in this CPG model were derived from electrophysiological and neuroanatomical reconstruction studies conducted in the rat brainstem-spinal cord in situ and on subnetworks isolated in living brainstem slice preparations in vitro with active circuits. These models also incorporated for the first time regulation of different circuit components by modeled afferent input signals from several critical neuromodulatory control systems that are known to be involved in regulation of respiratory pattern generation. For dynamical analysis of CPG network operation, methods from dynamical systems theory were also applied to identify critical dynamical variables and parameters of circuit operation that underlie respiratory rhythm and pattern generation and control the orderly transitions between the functionally distinct phases of inspiratory and expiratory neural activity. Computer simulations with the microcircuit and large-scale models mimicked many features of the single-cell and neuron population activity patterns found experimentally under different in vitro and in situ conditions. A major new hypothesis derived from experimental studies and tested with these models was that the capability to generate oscillatory activity exists within the respiratory CPG at multiple levels of cellular and network organization. Thus different mechanisms of respiratory rhythm generation can be functionally expressed in a brain state-dependent manner and underlie multiple respiratory motor behaviors, some of which occur under normal physiological conditions and others of which emerge under pathophysiological conductions such as during severe brain hypoxia (conditions of abnormally low oxygen). Simulations with models of different levels of cellular and network complexity confirmed the plausibility of this new concept and have provided insights into the essential cellular and network mechanisms involved. At the system level, models of the respiratory neural control system have been developed that couple these essential neural circuit dynamics with peripheral oxygen and carbon dioxide exchange, blood gas transport, and physiological feedback regulation of central respiratory circuits by signals such as blood/brain levels of oxygen and carbon dioxide. These latter models represent the first generation of system-level control models that integrate essential elements of nervous system structural-functional properties and realistic features of the respiratory gas exchange and transport system. All of these models are currently being applied to further explore principles of operation of brainstem respiratory circuits and control of respiratory activity including under various (patho)physiological conditions associated with disturbances of brain and body oxygen/carbon dioxide homeostasis.